On the Solution of the Monotone and Nonmonotone Linear Complementarity Problem by an Infeasible Interior-Point Algorithm

Abstract

The use of an Infeasible Interior-Point (IIP) algorithm [14] is investigated for the solution of the Linear Complementarity Problem (LCP). Some monotone an nonmonotone LCPs from different sources are solved by two versions of the IIP algorithm, which differ in the line-search technique that computes the stepsize. The first version, denoted by SIPP, employs the simple maximum ratio technique commonly used in IIP methods for linear programming. On the other hand the second variant (GIIP) incorporates a more sophisticated Armijo-type line-search technique, that ensures global convergence for the procedure under some hypotheses. The computational experiments indicate that both the variants process efficiently monotone LCPs and LCPs with P matrices. On the contrary, the algorithms face many difficulties for solving some LCPs with P o matrices and LCPs associated with zero-sum bimatrix games. However, the algorithm GIIP has succeeded in a large number of these problems than the method SIPP.